Statistics and Probability Answers

The manager of a local gym has determined that the length of time patrons spend at the gym is a normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.

What proportion of patrons spend more than two hours at the gym?

Q: The manager of a local gym has determined that the length of time patrons spend at the gym is a normally distributed variable with a mean of 80 minutes and a standard deviation of 20 minutes.

a)What proportion of patrons spend more than two hours at the gym?

b)What proportion of patrons spend less than one hour at the gym?

c)What is the least amount of time spent by 60% of patrons at the gym?

1. The teacher would like to find out if there is significant difference in the performance of the male and female students in 35 item test in English. He wants to consider 0.5% level of significance. The result is shown below:

MALE STUDENTS

sample size = 8

sample mean = 24.27

standard deviation = 9.36

FEMALE STUDENTS

sample size = 7

sample mean = 21.07

standard deviation = 8.25

in the game of bridge each of 4 players is dealt 13 cars from an ordinary well-shuffled deck of 52 cards. Find the probability that one of the players gets a) 7 diamonds, 2 clubs, 3 hearts, and one spade, b) a complete suit, c) 9 cards are of one suit

Given the following situations, write A, if it is two-tailed, B if one-tailed (left-

tailed), and C if one-tailed (right-tailed). (10 points)

1. Research on processed foods lessens the life span of a person.

2. A government official claims that the dropout rate for local schools is 25%.

3. A civil engineer is trying to prove that his new method of laying blocks is more

effective than the traditional method.

4. A new stockbroker, named XYZ, claims that their brokerage fees are lower than

that of the current fee.

5. A government official claims that the dropout rate for local schools is 25%.

Given the following situations, write A, if it is two-tailed, B if one-tailed (left-tailed), and C if one-tailed (right-tailed). (10 points)

1. A mother wants to prove that listening to classical music improves children's thinking process.

2. The principal of a certain school claims that the dropout rate for the certain municipality is higher than 25%.

3. Research on whether computer aided instruction is the same as lecture method

of a lesson presentation.

4. Research on smoking lessens the life span of a person.

5. Determine whether the mean monthly salary of call center agents is 25,000 a

month.

A. State the null hypothesis (𝐻𝑜) and the alternative hypothesis (𝐻𝑎) for each

of the following. (10 points)

1. A medical trial is conducted to test whether or not a new medicine reduces

cholesterol by 25%.

𝐻𝑜:

𝐻𝑎:

2. We want to test whether the mean GPA of students in a certain college is different

from 2.0 (out of 4.0).

3. We want to test if college students take less than five years to graduate from

college, on the average.

𝐻𝑜:

𝐻𝑎:

4. On a state driver’s test, about 40% pass the test on the first try. We want to test if

more than 40% pass on the first try.

𝐻𝑜:

𝐻𝑎:

5. A research on whether computer aided instruction is better than lecture method

of a lesson presentation.

𝐻𝑜:

𝐻𝑎:

According to the school librarian, the average number of pages of books in the reference section is 240. To

test her claim, she collected a sample of 15 books and after noting the number of pages of each book, she

determined that the mean number of pages is 224.6 with a standard deviation of 4.1. At α = 0.01, will the

librarian be able to prove her claim?

the subject group head of shs mathematics department announced that the mean percentage score of grade 11 learning in the 3rd quarter grade in statistic and probability was it in 9 in the standard deviation was 12 one learned who believed that the mean percentage score was less than this randomly selected 34 learner in computed their mean scores obtained a mean percentage score of 85 at 0.01 level of significance test the learners belief